In the field of tracking systems employed for tracking satellites, missiles, and the like, it is the object of the apparatus and methods employed therein to provide accurate tracking information about the tracked object. While radar is useful for slower moving objects in providing ranging information, tracking systems employed with, for example, Global Positioning Systems (GPS), space probes under dynamics, the Space Shuttle, space stations, satellite communications, and the like, must provide more information and more accurate information, all under extremely adverse conditions. For example, a rocket (both outgoing and incoming) is typically under high dynamic forces imparting rapid acceleration and increases in velocity.
In a great many cases in the area of interest, the tracked object is emitting a detectable radio frequency (RF) signal. Most often, the RF signal is the carrier for digital information being relayed to a ground station. As is well known, any alternating signal will be effected by the Doppler effect of its movement. Thus, a siren on a vehicle operating at a fixed audio frequency will appear to be at a higher frequency when approaching a point at a fixed velocity and will appear to be at a lower frequency when moving away from the same point at the same fixed velocity. If the vehicle is under acceleration, the frequency (and therefore the tone) of the siren will appear to be increasing and vice versa when in a state of deceleration. With respect to object tracking, the Doppler effect on an emitted detectable frequency can be put to good use in deriving speed and acceleration data about the object employing known mathematical techniques and a computer's rapid computational power.
Where the speeds and dynamics involved are not in the excess, well known prior art techniques have been employed to perform the data analysis on the received signal as sampled to provide the data which is analyzed. Thus, phase-locked loops or extended Kalman filters are commonly employed in the prior art for carrier phase estimation. Likewise, a Fast Fourier Transform (FFT) is a commonly employed mathematical technique. Where the parameters involved are in the excess as in the case of a very high dynamic GPS receiver, these prior art techniques simply do not operate. For example, FFT requires a 30dB-Hz (1000:1) signal power-to-noise spectral density ratio (SNR) or better to provide accurate results. Under the high dynamics and the sample sizes in the environment of interest, such a SNR is not possible so FFT analysis is not possible.
The problem can possibly best be understood by reference to the simplified waveform and timing diagram of FIG. 1. As will be recalled, the typical signal 10 comprises an alternating waveform carrier with binary data impressed thereon. If the binary data were not present, the analysis of the signal 10 would not be a problem as the sample period could be sufficiently long to provide a high enough SNR for standard analysis techniques and circuitry to be effective. Such is not the case, however. For example, the signal 10 of FIG. 1 depicts a portion representing the binary sequence 101. Because of the spacing of the binary data on the signal 10, the signal 10 must be sampled during sampling periods (T.sub.b) 12 of limited length. During each period (T.sub.b) typically ten to twenty samples are taken. This cannot provide a sufficiently high SNR for FFT, for example. As can be seen from FIG. 1, as the signal 10 changes from representing the first "1" to the "0", the phase of the signal 10 shifts 180.degree. . This phase shift occurs close adjacent the end of the first sample period (T.sub.b) 12 designated as "T.sub.b ". A similar phase shift occurs close adjacent the end of the second sample period (T.sub.b) 12 designated as "2T.sub.b " where the signal 10 changes from representing the "0" to the second "1". It is this change in phase as the signal 10 changes between "1" and "0" states which prevents the signal 10 from being analyzed for more than one sample period 12. Thus, since the sample periods 12 are not long enough to produce the required SNR for conventional analysis methods and apparatus, they cannot be used in this environment to produce reliable and accurate results.
The problem of estimating the parameters of a received quasi sinusoidal signal in the presence of noise has received considerable attention in the literature; however, for the case when the received carrier is modulated by unknown data and simultaneously experiences considerably high Doppler and Doppler rate, the research reported in the published literature is somewhat limited. One proposed prior art approach which has been analyzed for the GPS application is an estimator structure based on the maximum likelihood estimation (MLE) of code delay and Doppler frequency over a single data bit period. The "pseudo" estimates over different bit intervals are combined by a Kalman filter to provide tracking of Doppler frequency. By limiting the primary (ML) estimation period to less than one data bit period, the problem of detecting the data bits is bypassed; however, perhaps due to such a limitation and also due to high frequency rate involved (not explicitly estimated by the MLE), a threshold of about 30 dB-Hz in terms of the received carrier power-to-noise power spectral density ratio (P/N.sub.o) was obtained. Due to the lack of knowledge of the data bits, phase estimation is not feasible by this scheme.
In terms of GPS applications, the problem of data modulation can be overcome by establishing a parallel (non-dynamic) link between the GPS satellites and a control ground receiver which also simultaneously receives the frequency translated version of the GPS signals. The data demodulation and estimation is then performed at the ground receiver. Once the data modulation is removed from the GPS receiver signal, the problem reduces to simply estimating the phase, frequency, etc., of an unmodulated RF carrier. This latter problem, of course, has been studied extensively in the literature.
In the literature describing the prior art, there are several techniques of data detection. If the signal waveform is known precisely and does not change from bit to bit, the data can be detected coherently by using matched filters or correlation receivers, irrespective of the actual waveform. If the waveform (carrier) has a constant known frequency, either a coherent or a differentially coherent detection can be employed, depending upon whether or not the phase of the carrier is known. In a decision-directed version of these techniques, the carrier phase and/or frequency are estimated by a phase-locked loop technique and the data detector becomes part of the loop. It is clear that these techniques most likely will not be feasible under the low SNR and high dynamics of the required environment in that the frequency may not be even nearly constant over the detection period and under such low SNR conditions that it may not be possible to acquire the lock with data modulation present.
In an alternate solution as in the Costas loop, the data detection problem is bypassed by a multiplicative technique; however, such a loop also suffers in terms of loss of SNR due to the multiplicative noise term which can be excessive for the high loop filter bandwidths required and the low received SNR.
It is thus apparent that schemes which incorporate data detection in a loop which in turn is made dependent upon the acquisition and tracking of the loop may not be desirable under such high dynamic conditions since the loop may not acquire to start with and may lose lock during tracking. Therefore, what is needed is a technique where data can be detected even under open loop condition.